Electric Field of Uniformly Charged Ring: Derivation Explained

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Discussion Overview

The discussion centers on the derivation of the electric field for a uniformly charged ring, specifically focusing on the expression for the electric field along its symmetry axis and the subsequent differentiation of that expression with respect to the axial distance.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the electric field expression as E=kqz/(z²+R²)^(3/2) and seeks clarification on how to derive the expression for its derivative.
  • Another participant requests details on what the original poster has attempted in their derivation and notes the context of the electric field being specific to points along the symmetry axis of the ring.
  • A participant shares their own derivative calculation, arriving at a different form and expresses confusion about simplifications made in the book.
  • There is a correction regarding the numerator of the derivative, with one participant acknowledging a mistake in their earlier expression.
  • A later reply confirms the derivative form using product and chain rules without simplifications, prompting further exploration of combining expressions.
  • Ultimately, the original poster confirms they have successfully derived the result with assistance from another participant.

Areas of Agreement / Disagreement

Participants generally agree on the steps involved in deriving the electric field and its derivative, but there are variations in the expressions used, particularly regarding the terms in the numerator. The discussion reflects a collaborative effort to clarify and refine the derivation process without a definitive consensus on the simplifications.

Contextual Notes

The discussion involves assumptions about the application of differentiation rules and the specific context of the electric field's derivation, which may not be fully detailed in the initial posts.

dido28
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hi every one on an exercise on book we ask us to find the electrical field for a uniformly charged ring where we going to find : E=kqz/(z2+R2)3/2
then we have to derivate it wth respect to z and we find : dE/dz=kq*(R2+2z2)/(z2+R2)5/2
so my question is how do we get this derivation ?
 
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You will have show us what you have *tried* thus far. Where did you get stuck in the derivation when you tried it yourself? Also note that the given expression is only the electric field produced by the uniformly charged static ring at points along its symmetry axis (in case you didn't know already).
 
well me i found : dE/dz=qk[ (z2+R2)3/2-3z2(z2+R2)-1/2 ]/(z2+R2)3
i just applied the rule that i know but in the book it seems that they did some simplification so my question is how they did this
 
Oh are you only interested in finding the derivative? Do you already know how to get the electric field itself?
 
yes that's it
 
Are you sure it wasn't ##R^2 - 2z^2## as opposed to ##R^2 + 2z^2## in the numerator of the final answer?
 
oh yes sorry it's R2-2z2 :shy:
 
Ok. Would you agree that, before doing any simplifications, the derivative comes out to ##\frac{\mathrm{d} E}{\mathrm{d} z} = \frac{kq}{(z^2 + R^2)^{3/2}} - \frac{3kqz^2}{(z^2 + R^2)^{5/2}}##? All I have done is use the product and chain rule; I haven't done any simplifications at all. Now, can you find a way to combine these two expressions?
 
yes it's done i get the result . thanks for your help WannabeNewton
 
  • #10
I didn't do anything mate! It was all you :) Good luck with your studies.
 

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